Numerical investigation of the linear evolution of Tollmien–Schlichting waves over longitudinal riblet surface

Abstract

The effect of longitudinal riblets on the spatially developing Tollmien–Schlichting (T–S) waves within the boundary layer is numerically investigated by direct numerical simulation. The riblets, designed to reduce turbulent drag and featuring a blade-like shape with zero thickness, are the primary focus. Part of the flat plate is replaced by riblet surface, and T–S waves with varying frequencies are introduced prior to the onset of the riblets. Moreover, the influence of riblet size is further discussed, and the underlying mechanism by which riblets affect T–S waves is identified based on the analysis of disturbance energy equation. The results demonstrate that the presence of riblets significantly enhances the growth of T–S waves. The modulation of base flow by riblets results in the emergence of an inflection point in the velocity profile within the boundary layer, thereby enhancing the flow instability. The growth rate of T–S waves and the unstable region on the riblet surface are observed to be considerably amplified, and an increase in riblet's lateral spacing and height to spacing ratio intensifies this amplification. From the perspective of disturbance energy, it is shown that although riblets cause additional energy dissipation in their vicinity, their modification of the mean velocity gradient and the phase difference between streamwise and wall-normal velocity fluctuations contribute to a significant increase in the production term, which consequently accelerates the growth of T–S waves.